ON THE MEASURABILITY FOR FUNCTIONAL OF EMPIRICAL PROCESSES

In this paper, we give some results for checking the measurability of functional of empirical processes, their direct applications concern with the measurability of statis-tics constructed by Projection pursuit technique, thus the results obtained provide a basis in theory for projection pursuit study.

Drilling-based measuring method for the c-φ parameter of rock and its field application

The technology of drilling tests makes it possible to obtain the strength parameter of rock accurately in situ. In this paper, a new rock cutting analysis model that considers the influence of the rock crushing zone(RCZ) is built. The formula for an ultimate cutting force is established based on the limit equilibrium principle. The relationship between digital drilling parameters(DDP) and the c-φ parameter(DDP-cφ formula, where c refers to the cohesion and φ refers to the internal friction angle) is derived, and the response of drilling parameters and cutting ratio to the strength parameters is analyzed. The drillingbased measuring method for the c-φ parameter of rock is constructed. The laboratory verification test is then completed, and the difference in results between the drilling test and the compression test is less than 6%. On this basis, in-situ rock drilling tests in a traffic tunnel and a coal mine roadway are carried out, and the strength parameters of the surrounding rock are effectively tested. The average difference ratio of the results is less than 11%, which verifies the effectiveness of the proposed method for obtaining the strength parameters based on digital drilling. This study provides methodological support for field testing of rock strength parameters.

Several applications of the theory of random conjugate spaces to measurability problems

The central purpose of this paper is to illustrate that combining the recently developed theory of random conjugate spaces and the deep theory of Banach spaces can, indeed, solve some difficult measurability problems which occur in the recent study of the Lebesgue (or more general, Orlicz)-Bochner function spaces as well as in a slightly different way in the study of the random functional analysis but for which the measurable selection theorems currently available are not applicable. It is important that this paper provides a new method of studying a large class of the measurability problems, namely first converting the measurability problems to the abstract existence problems in the random metric theory and then combining the random metric theory and the relative theory of classical spaces so that the measurability problems can be eventually solved. The new method is based on the deep development of the random metric theory as well as on the subtle combination of the random metric theory with classical space theory.

Construction and Regularity of Transition Functions on Polish Spaces under Measurability Conditions

This paper concerns the construction and regularity of a transition （probability） function of a nonhomogeneous continuous-time Maxkov process with given transition rates and a general state space. Motivating from a lot of restriction in applications of a transition function with continuous （in t ≥0） and consewative transition rates q（t, x, A）, we consider the case that q（t, x, A） axe only required to satisfy a mild measurability （in t ≥ O） condition, which is a generalization of the continuity condition. Under the measurability condition we construct a transition function with the given transition rates, provide a necessary and sufficient condition for it to be regular, and further obtain some interesting additional results.

Bunch-length measurement at a bunch-by-bunch rate based on time–frequency-domain joint analysis techniques and its application

This paper presents a new technique for measuring the bunch length of a high-energy electron beam at a bunch-by-bunch rate in storage rings.This technique uses the time–frequency-domain joint analysis of the bunch signal to obtain bunch-by-bunch and turn-by-turn longitudinal parameters,such as bunch length and synchronous phase.The bunch signal is obtained using a button electrode with a bandwidth of several gigahertz.The data acquisition device was a high-speed digital oscilloscope with a sampling rate of more than 10 GS/s,and the single-shot sampling data buffer covered thousands of turns.The bunch-length and synchronous phase information were extracted via offline calculations using Python scripts.The calibration coefficient of the system was determined using a commercial streak camera.Moreover,this technique was tested on two different storage rings and successfully captured various longitudinal transient processes during the harmonic cavity debugging process at the Shanghai Synchrotron Radiation Facility(SSRF),and longitudinal instabilities were observed during the single-bunch accumulation process at Hefei Light Source(HLS).For Gaussian-distribution bunches,the uncertainty of the bunch phase obtained using this technique was better than 0.2 ps,and the bunch-length uncertainty was better than 1 ps.The dynamic range exceeded 10 ms.This technology is a powerful and versatile beam diagnostic tool that can be conveniently deployed in high-energy electron storage rings.

Beyond functional MRI signals:molecular and cellular modifiers of the functional connectome and cognition

Our brain is constantly active.Even at rest,the brain carries out essential functions such as maintenance of resting potentials,subthreshold synaptic activity,and spiking activity related to information processing.This resting activity can be assessed with several in vivo tools,such as resting-state functional magnetic resonance imaging.This technique measures subtle changes in blood flow,volume,and oxygenation that occur over time.Although vascular in nature,resting-state functional magnetic resonance imaging is considered a reliable proxy of neural activity and several studies have shown that the brain is functionally divided into interacting neural networks called the“functional connectome”.

FPGA and computer-vision-based atom tracking technology for scanning probe microscopy

Atom tracking technology enhanced with innovative algorithms has been implemented in this study,utilizing a comprehensive suite of controllers and software independently developed domestically.Leveraging an on-board field-programmable gate array(FPGA)with a core frequency of 100 MHz,our system facilitates reading and writing operations across 16 channels,performing discrete incremental proportional-integral-derivative(PID)calculations within 3.4 microseconds.Building upon this foundation,gradient and extremum algorithms are further integrated,incorporating circular and spiral scanning modes with a horizontal movement accuracy of 0.38 pm.This integration enhances the real-time performance and significantly increases the accuracy of atom tracking.Atom tracking achieves an equivalent precision of at least 142 pm on a highly oriented pyrolytic graphite(HOPG)surface under room temperature atmospheric conditions.Through applying computer vision and image processing algorithms,atom tracking can be used when scanning a large area.The techniques primarily consist of two algorithms:the region of interest(ROI)-based feature matching algorithm,which achieves 97.92%accuracy,and the feature description-based matching algorithm,with an impressive 99.99%accuracy.Both implementation approaches have been tested for scanner drift measurements,and these technologies are scalable and applicable in various domains of scanning probe microscopy with broad application prospects in the field of nanoengineering.

A seismic elastic moduli module for the measurements of low-frequency wave dispersion and attenuation of fluid-saturated rocks under different pressures

Knowledge about the seismic elastic modulus dispersion,and associated attenuation,in fluid-saturated rocks is essential for better interpretation of seismic observations taken as part of hydrocarbon identification and time-lapse seismic surveillance of both conventional and unconventional reservoir and overburden performances.A Seismic Elastic Moduli Module has been developed,based on the forced-oscillations method,to experimentally investigate the frequency dependence of Young's modulus and Poisson's ratio,as well as the inferred attenuation,of cylindrical samples under different confining pressure conditions.Calibration with three standard samples showed that the measured elastic moduli were consistent with the published data,indicating that the new apparatus can operate reliably over a wide frequency range of f∈[1-2000,10^(6)]Hz.The Young's modulus and Poisson's ratio of the shale and the tight sandstone samples were measured under axial stress oscillations to assess the frequency-and pressure-dependent effects.Under dry condition,both samples appear to be nearly frequency independent,with weak pressure dependence for the shale and significant pressure dependence for the sandstone.In particular,it was found that the tight sandstone with complex pore microstructure exhibited apparent dispersion and attenuation under brine or glycerin saturation conditions,the levels of which were strongly influenced by the increased effective pressure.In addition,the measured Young's moduli results were compared with the theoretical predictions from a scaled poroelastic model with a reasonably good agreement,revealing that the combined fluid flow mechanisms at both mesoscopic and microscopic scales possibly responsible for the measured dispersion.

Development of a toroidal soft x-ray imaging system and application for investigating three-dimensional plasma on J-TEXT

A toroidal soft x-ray imaging(T-SXRI)system has been developed to investigate threedimensional(3D)plasma physics on J-TEXT.This T-SXRI system consists of three sets of SXR arrays.Two sets are newly developed and located on the vacuum chamber wall at toroidal positionsφof 126.4°and 272.6°,respectively,while one set was established previously atφ=65.50.Each set of SXR arrays consists of three arrays viewing the plasma poloidally,and hence can be used separately to obtain SXR images via the tomographic method.The sawtooth precursor oscillations are measured by T-SXRI,and the corresponding images of perturbative SXR signals are successfully reconstructed at these three toroidal positions,hence providing measurement of the 3D structure of precursor oscillations.The observed 3D structure is consistent with the helical structure of the m/n=1/1 mode.The experimental observation confirms that the T-SXRI system is able to observe 3D structures in the J-TEXT plasma.

Triple-path feature transform network for ring-array photoacoustic tomography image reconstruction

Photoacoustic imaging(PAI)is a noninvasive emerging imaging method based on the photoacoustic effect,which provides necessary assistance for medical diagnosis.It has the characteristics of large imaging depth and high contrast.However,limited by the equipment cost and reconstruction time requirements,the existing PAI systems distributed with annular array transducers are difficult to take into account both the image quality and the imaging speed.In this paper,a triple-path feature transform network(TFT-Net)for ring-array photoacoustic tomography is proposed to enhance the imaging quality from limited-view and sparse measurement data.Specifically,the network combines the raw photoacoustic pressure signals and conventional linear reconstruction images as input data,and takes the photoacoustic physical model as a prior information to guide the reconstruction process.In addition,to enhance the ability of extracting signal features,the residual block and squeeze and excitation block are introduced into the TFT-Net.For further efficient reconstruction,the final output of photoacoustic signals uses‘filter-then-upsample’operation with a pixel-shuffle multiplexer and a max out module.Experiment results on simulated and in-vivo data demonstrate that the constructed TFT-Net can restore the target boundary clearly,reduce background noise,and realize fast and high-quality photoacoustic image reconstruction of limited view with sparse sampling.

MULTIPLE INTERSECTIONS OF SPACE-TIME ANISOTROPIC GAUSSIAN FIELDS

Let X={X(t)∈R^(d),t∈R^(N)}be a centered space-time anisotropic Gaussian field with indices H=(H_(1),…,H_(N))∈(0,1)~N,where the components X_(i)(i=1,…,d)of X are independent,and the canonical metric√(E(X_(i)(t)-X_(i)(s))^(2))^(1/2)(i=1,…,d)is commensurate with■for s=(s_(1),…,s_(N)),t=(t_(1),…,t_(N))∈R~N,α_(i)∈(0,1],and with the continuous functionγ(·)satisfying certain conditions.First,the upper and lower bounds of the hitting probabilities of X can be derived from the corresponding generalized Hausdorff measure and capacity,which are based on the kernel functions depending explicitly onγ(·).Furthermore,the multiple intersections of the sample paths of two independent centered space-time anisotropic Gaussian fields with different distributions are considered.Our results extend the corresponding results for anisotropic Gaussian fields to a large class of space-time anisotropic Gaussian fields.

A global model of intensity autocorrelation to determine laser pulse duration

We present a new global model of collinear autocorrelation based on second harmonic generation nonlinearity.The model is rigorously derived from the nonlinear coupled wave equation specific to the autocorrelation measurement configuration,without requiring a specific form of the incident pulse function.A rigorous solution of the nonlinear coupled wave equation is obtained in the time domain and expressed in a general analytical form.The global model fully accounts for the nonlinear interaction and propagation effects within nonlinear crystals,which are not captured by the classical local model.To assess the performance of the global model compared to the classic local model,we investigate the autocorrelation signals obtained from both models for different incident pulse waveforms and different full-widthes at half-maximum(FWHMs).When the incident pulse waveform is Lorentzian with an FWHM of 200 fs,the global model predicts an autocorrelation signal FWHM of 399.9 fs,while the classic local model predicts an FWHM of 331.4 fs.The difference between the two models is 68.6 fs,corresponding to an error of 17.2%.Similarly,for a sech-type incident pulse with an FWHM of 200 fs,the global model predicts an autocorrelation signal FWHM of 343.9 fs,while the local model predicts an FWHM of 308.8 fs.The difference between the two models is 35.1 fs,with an error of 10.2%.We further examine the behavior of the models for Lorentzian pulses with FWHMs of 100 fs,200 fs and 500 fs.The differences between the global and local models are 17.1 fs,68.6 fs and 86.0 fs,respectively,with errors approximately around 17%.These comparative analyses clearly demonstrate the superior accuracy of the global model in intensity autocorrelation modeling.

Forward modelling of the Cotton-Mouton effect polarimetry on EAST tokamak

Measurement of plasma electron density by far-infrared laser polarimetry has become a routine and indispensable tool in magnetic confinement fusion research.This article presents the design of a Cotton-Mouton polarimeter interferometer,which provides a reliable density measurement without fringe jumps.Cotton-Mouton effect on Experimental Advanced Superconducting Tokamak(EAST)is studied by Stokes equation with three parameters(s_(1),s_(2),s_(3)).It demonstrates that under the condition of a small Cotton-Mouton effect,parameter s_(2)contains information about Cotton-Mouton effect which is proportional to the line-integrated density.For a typical EAST plasma,the magnitude of Cotton-Mouton effects is less than 2πfor laser wavelength of 432μm.Refractive effect due to density gradient is calculated to be negligible.Time modulation of Stokes parameters(s_(2),s_(3))provides heterodyne measurement.Due to the instabilities arising from laser oscillation and beam refraction in plasmas,it is necessary for the system to be insensitive to variations in the amplitude of the detection signal.Furthermore,it is shown that non-equal amplitude of X-mode and O-mode within a certain range only affects the DC offset of Stokes parameters(s_(2),s_(3))but does not greatly influence the phase measurements of Cotton-Mouton effects.

One-step quantum dialogue

Quantum dialogue(QD)enables two communication parties to directly exchange secret messages simultaneously.In conventional QD protocols,photons need to transmit in the quantum channel for two rounds.In this paper,we propose a one-step QD protocol based on the hyperentanglement.With the help of the non-local hyperentanglement-assisted Bell state measurement(BSM),the photons only need to transmit in the quantum channel once.We prove that our one-step QD protocol is secure in theory and numerically simulate its secret message capacity under practical experimental condition.Compared with previous QD protocols,the one-step QD protocol can effectively simplify the experiment operations and reduce the message loss caused by the photon transmission loss.Meanwhile,the non-local hyperentanglement-assisted BSM has a success probability of 100%and is feasible with linear optical elements.Moreover,combined with the hyperentanglement heralded amplification and purification,our protocol is possible to realize long-distance one-step QD.

Fast compressed sensing spectral measurement with adaptive gradient multiscale resolution

We propose a fast,adaptive multiscale resolution spectral measurement method based on compressed sensing.The method can apply variable measurement resolution over the entire spectral range to reduce the measurement time by over 75%compared to a global high-resolution measurement.Mimicking the characteristics of the human retina system,the resolution distribution follows the principle of gradually decreasing.The system allows the spectral peaks of interest to be captured dynamically or to be specified a priori by a user.The system was tested by measuring single and dual spectral peaks,and the results of spectral peaks are consistent with those of global high-resolution measurements.

Statistical Channel Modeling for Indoor VLC Communications Based on Channel Measurements

Visible light communication(VLC)has attracted much attention in the research of sixthgeneration(6G)systems.Furthermore,channel modeling is the foundation for designing efficient and robust VLC systems.In this paper,we present extensive VLC channel measurement campaigns in indoor environments,i.e.,an office and a corridor.Based on the measured data,the large-scale fading characteristics and multipath-related characteristics,including omnidirectional optical path loss(OPL),K-factor,power angular spectrum(PAS),angle spread(AS),and clustering characteristics,are analyzed and modeled through a statistical method.Based on the extracted statistics of the above-mentioned channel characteristics,we propose a statistical spatial channel model(SSCM)capable of modeling multipath in the spatial domain.Furthermore,the simulated statistics of the proposed model are compared with the measured statistics.For instance,in the office,the simulated path loss exponent(PLE)and the measured PLE are 1.96and 1.97,respectively.And,the simulated medians of AS and measured medians of AS are 25.94°and 24.84°,respectively.Generally,the fact that the simulated results fit well with measured results has demonstrated the accuracy of our SSCM.

Finesse measurement for high-power optical enhancement cavity

Finesse is a critical parameter for describing the characteristics of an optical enhancement cavity(OEC). This paper first presents a review of finesse measurement techniques, including a comparative analysis of the advantages, disadvantages, and potential limitations of several main methods from both theoretical and practical perspectives. A variant of the existing method called the free spectral range(FSR) modulation method is proposed and compared with three other finesse measurement methods, i.e., the fast-switching cavity ring-down(CRD) method, the rapidly swept-frequency(SF) CRD method, and the ringing effect method. A high-power OEC platform with a high finesse of approximately 16000 is built and measured with the four methods. The performance of these methods is compared, and the results show that the FSR modulation method and the fast-switching CRD method are more suitable and accurate than the other two methods for high-finesse OEC measurements. The CRD method and the ringing effect method can be implemented in open loop using simple equipment and are easy to perform. Additionally, recommendations for selecting finesse measurement methods under different conditions are proposed, which benefit the development of OEC and its applications.

Sharing quantum nonlocality in the noisy scenario

It was showed in [Phys. Rev. Lett. 125 090401(2020)] that there exist unbounded number of independent Bobs who can share quantum nonlocality with a single Alice by performing sequentially measurements on the Bob's half of the maximally entangled pure two-qubit state. However, from practical perspectives, errors in entanglement generation and noises in quantum measurements will result in the decay of nonlocality in the scenario. In this paper, we analyze the persistency and termination of sharing nonlocality in the noisy scenario. We first obtain the two sufficient conditions under which there exist n independent Bobs who can share nonlocality with a single Alice under noisy measurements and the noisy initial two qubit entangled state. Analyzing the two conditions, we find that the influences on persistency under different kinds of noises can cancel each other out. Furthermore, we describe the change patterns of the maximal nonlocality-sharing number under the influence of different noises. Finally, we extend our investigation to the case of arbitrary finite-dimensional systems.

Measuring small longitudinal phase shifts via weak measurement amplification

Weak measurement amplification,which is considered as a very promising scheme in precision measurement,has been applied to various small physical quantities estimations.Since many physical quantities can be converted into phase signals,it is interesting and important to consider measuring small longitudinal phase shifts by using weak measurement.Here,we propose and experimentally demonstrate a novel weak measurement amplification-based small longitudinal phase estimation,which is suitable for polarization interferometry.We realize one order of magnitude amplification measurement of a small phase signal directly introduced by a liquid crystal variable retarder and show that it is robust to the imperfection of interference.Besides,we analyze the effect of magnification error which is never considered in the previous works,and find the constraint on the magnification.Our results may find important applications in high-precision measurements,e.g.,gravitational wave detection.

Power equipment vibration visualization using intelligent sensing method based on event-sensing principle

Vibration measurements can be used to evaluate the operation status of power equipment and are widely applied in equipment quality inspection and fault identification.Event-sensing technology can sense the change in surface light intensity caused by object vibration and provide a visual description of vibration behavior.Based on the analysis of the principle underlying the transformation of vibration behavior into event flow data by an event sensor,this paper proposes an algorithm to reconstruct event flow data into a relationship correlating vibration displacement and time to extract the amplitude-frequency characteristics of the vibration signal.A vibration measurement test platform is constructed,and feasibility and effectiveness tests are performed for the vibration motor and other power equipment.The results show that event-sensing technology can effectively perceive the surface vibration behavior of power and provide a wide dynamic range.Furthermore,the vibration measurement and visualization algorithm for power equipment constructed using this technology offers high measurement accuracy and efficiency.The results of this study provide a new noncontact and visual method for locating vibrations and performing amplitude-frequency analysis on power equipment.